Can't remember how to do this simple definite integral

In summary, to find the integral of a simple function, you can use basic integration rules such as the power rule, product rule, and sum rule. The definite integral of a function represents the area under the curve within a specific interval and can be evaluated using the Fundamental Theorem of Calculus or numerical methods. Some common mistakes when solving definite integrals include forgetting to add the constant of integration and errors in algebraic simplification. To improve your skills in solving definite integrals, practice with a variety of integrals using different techniques and review basic integration rules. Seeking guidance from a tutor or studying with a group can also be helpful.
  • #1
astonmartin
23
0
If my Force = (-gamma)(dx/dt)
velocity v = dx/dt
Mass m

(m)(dv/dt) = F = (-gamma)(dx/dt)

Now I want to integrate it over kT<= t <= (k+1)T

Rearranging gives me (dv/v) = (-gamma/m)dt

The right side integrates to (-gamma/m)(T), but how do I integrate the left side over kT<= t <= (k+1)T??

Thanks
 
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  • #2
[tex]\int \frac{1}{v} dv= ln(v)+ C[/tex]
 
  • #3
^but what does that give me for the definite integral?

ln [v(k+1)T / v(kT)] ?
 

1. How do I find the integral of a simple function?

To find the integral of a simple function, you can use the basic integration rules such as the power rule, product rule, and sum rule. You can also use integration by parts or substitution to solve more complex integrals.

2. What is the definite integral of a function?

The definite integral of a function is a number that represents the area under the curve of the function within a specific interval. It is denoted by ∫f(x)dx, where f(x) is the function and dx is the differential of the variable x.

3. How do I evaluate a definite integral?

To evaluate a definite integral, you can use the Fundamental Theorem of Calculus, which states that the definite integral of a function can be evaluated by finding its antiderivative and plugging in the upper and lower limits of the interval. You can also use numerical methods such as the trapezoidal rule or Simpson's rule to approximate the value of the integral.

4. What are some common mistakes when solving definite integrals?

Some common mistakes when solving definite integrals include forgetting to add the constant of integration, incorrect use of integration rules, and errors in algebraic simplification. It is important to double check your work and be careful with your calculations when solving integrals.

5. How can I improve my skills in solving definite integrals?

To improve your skills in solving definite integrals, you can practice solving a variety of integrals using different techniques. You can also review basic integration rules and make sure you understand the concepts behind them. It can also be helpful to seek guidance from a tutor or study with a group to work on integrals together.

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